Spray large pot over medium heat and spray with nonstick cooking spray. Saute onions and carrots with salt and pepper until onions are mostly translucent. Stir in garlic and cook another minute until fragrant.: You should smell the sweet, savory aroma of softened onion and the warm perfume of garlic as they cook in a lightly oiled pot. The sound is a gentle sizzle, and visually the onion will go from opaque to mostly translucent, with the carrot softening but still holding shape. This step builds the flavor foundation, so take your time over medium heat rather than rushing to high heat which can brown the aromatics and create bitterness. A common mistake is overheating the pan; if the edges begin to brown too quickly, lower the heat and stir more frequently to keep everything evenly soft and glossy.
Add in chicken broth, salt, pepper, tarragon, bay leaves and chicken breasts whole. Cover and bring to boil, then crack the lid and reduce to simmer until chicken breasts are thoroughly cooked. (Depending how thick your chicken breasts are, this can take anywhere between 15-30 minutes.): As the chicken broth comes up to a boil you will see gentle rolling bubbles; cracking the lid slightly prevents an aggressive boil that can toughen the chicken . The aromatics and herbs will perfume the liquid, and the surface will show faint flecks of seasoning. Simmering gently lets the meat cook evenly and stay moist, which makes shredding easy. Watch for a steady simmer rather than a hard boil, and avoid leaving it unattended, since overcooked chicken becomes dry and stringy.
While chicken is cooking, whisk evaporated milk with flour until smooth.: When you whisk the cold evaporated milk and flour together, you should end up with a silky, lump free batter. The mixture should be completely smooth and slightly thickened, resembling a thin paste. This pre blending prevents lumps when it hits the hot broth. If you add flour directly to hot liquid you risk clumps forming, so take the extra minute to combine them thoroughly. A common pitfall is not whisking long enough, leaving grainy bits that will remain in the soup.
Once chicken is finished cooking, remove from pot and shred. Replace back into pot. Add gnocchi and evaporated milk-flour mixture and bring to a simmer. Stir constantly while it is thickening and then reduce heat to low once it has thickened completely-this process should take 5 minutes. The soup should have thickened and the gnocchi should be floating and finished cooking. Taste and add more salt and pepper if necessary. (I made this three times and always added more salt and pepper since the evaporated milk has no seasonings.) Remove bay leaves. Stir in spinach and heavy cream right before serving.: After removing the cooked chicken , shred it so the strands are bite sized and return them to the pot; this helps them soak up the broth. When you add the pre mixed milk and flour , the sound changes to a soft simmer and you will see the liquid slowly become glossy and thicker, clinging to a spoon. Stir constantly during thickening to prevent the bottom from catching and to ensure even cooking. Watch for the gnocchi to float and look plump, which signals doneness. Taste and adjust salt and pepper because the dairy base can be bland; a frequent misstep is under seasoning at this stage. Finally, removing the bay leaves and stirring in the chopped spinach and heavy cream off heat retains the bright green color and silky finish, avoiding any overcooking of the greens.
Divide equally between 8 bowls and serve hot.: The final pour should reveal a glossy, thickened broth dotted with shredded chicken and pillowy gnocchi . Serve immediately while the soup is steaming and aromatic, and the textures are at their peak. If you wait too long, the gnocchi will continue to absorb liquid and soften further, so plan to portion and enjoy promptly. A common oversight is letting the soup sit in the pot too long before serving, which dulls the brightness of the spinach and softens the gnocchi excessively.
